Who doesn't love Tales of Symphonia? XD

In terms of FF, I prefer VI.

^ Definitely this

Xenogears, I was amazed back in the PSOne days, epic as fuck!

Killzone 2 easily

Resident Evil 1 (Ps1)

As with every thread like this, how does anyone pick just one??

Anyway not an all time favorite but one I recently saw and liked a lot was https://www.youtube.com/watch?v=U-LsQq9y5jM

And one of the modern favorites is https://www.youtube.com/watch?v=cMdiqv99l2E
As far as oldies go https://www.youtube.com/watch?v=GitgbU3BDRY

Dark souls I cinematic.

I've always ended up watching these intros, starting with Warhammer 40,000: Dawn of War

Then there's the quirkiness of Red Alert (or just skip to 2:00 for Hell March):

And it may not seem like much now, but the intro to Return to Zork was huge:

DC Universe Online had a great opening. If only the game was half as good as the opening....